Calculating Capacitance for Pulsed Nitrogen Laser Design: Tips and Tricks

[TrolliOlli]

Homework Statement

You are part of an engineering research team that is designing a pulsed nitrogen laser. To create the high energy densities needed to operate such a laser, the electrical discharge from a high-voltage capacitor is used. Typically, the energy requirement per pulse (i.e., per discharge) is 96 J. Estimate the capacitance required if the discharge is to create a spark across a gap of about 0.93 cm. Assume that the dielectric breakdown of nitrogen is the same as the value for normal air.

I honestly am completely lost.

I know C = Q/V = Q/Ed and also the potential energy U = 1/2 CV^2 but I don't know what I can do with the variables I'm given to get either V or E.

 

[Delphi51]

This brings me back - I built a nitrogen laser in 1975 and used it's UV pulses to stimulate an experimental dye laser.

A high voltage is required to ionize the air in the spark gap; you'll need to look that up, perhaps in Wikipedia. Once it is ionized, the resistance is quite low and you can assume all the energy in the capacitor goes into the discharge. So your U = 1/2 CV² will do the job once you know the voltage required.

 

[Spinnor]

You know the energy required, 96J, and you can probably blindly use that number. The breakdown voltage of air is found via a Google search,

http://www.google.com/webhp?hl=en#h...w.,cf.osb&fp=dc20b2672385f007&biw=720&bih=426

which yields the following,

http://en.wikipedia.org/wiki/Electrical_breakdown

about 3E6 volts/m. You know the gap in cm so you should be able to calculate the voltage required to breakdown the nitrogen.